A great variety of appearances may be produced with the same arrangement of spectra. Any two adjacent spectra with the central beam (as _b_, _c_, _a_) will form equilateral triangles and give hexagonal markings. Or by stopping off all but _g_, _c_, _e_ (or _b_, _d_, _f_), we again have the spectra in the form of equilateral triangles; but as they are now further apart, the sides of the triangles in the two cases being as √3 : 1, the hexagons will be smaller and three times as numerous. Their sides will also be arranged at a different angle to those of the first set. The hexagons may be entirely obliterated by admitting only the spectra _g_, _c_, or _g_, _f_, or _b_, _f_, etc., when new lines will appear at right angles, or obliquely inclined, to the median line. By varying the combinations of the spectra, therefore, different figures of varying size and positions are produced, all of which cannot, of course, represent the true structure. Not only, however, may the appearance of particular structure be obliterated or created, but it may even be _predicted_ before being seen under the microscope. If the position and relative intensity of the spectra in any particular case are given, the character of the resultant image, in some instances, may be worked out by mathematical calculations. A remarkable instance of such a prediction is to be found in the case recorded by Mr. Stephenson, where a mathematical student who had never seen a diatom, worked out the purely mathematical result of the interference of the six spectra _b-g_ of Fig. 33 (identical with _P. angulatum_), giving the drawing copied in Fig. 34. The special feature was the small markings between the hexagons, which had not, before this time, been noticed on _P. angulatum_. On more closely scrutinizing a valve, stopping out the central beam and allowing the six spectra only to pass, the small markings were found actually to exist, though they were so faint they had previously escaped observation until the result of the mathematical deduction had shown that they _ought_ to be seen.
These experiments seem to show that diffraction plays a very essential part in the formation of microscopical images, since dissimilar structures give identical images when the differences of their diffractive effect is removed, and conversely similar structures may give dissimilar images when their diffractive images are made dissimilar. Whilst a purely dioptric image answers point for point to the object on the stage, and enables a safe inference to be drawn as to the actual nature of that object, the visible indications of minute structure in a microscopical image are not always or necessarily conformable to the real nature of the object examined, so that nothing more can safely be inferred from the image as presented to the eye, than the presence in the object of such structural peculiarities as will produce the particular diffraction phenomena on which these images depend.